arXiv research

Estimates for scalar curvature equations on Kähler manifolds with singularities.

Upper diameter bound for manifolds with positive scalar curvature.

This note relaxes conditions for Kähler metrics with bounded entropy and scalar curvature.

This paper is to study the conformal scalar curvature equation on complete noncompact Riemannian manifold of nonpositive curvature. We derive some estimates and properties of supersolutions of the scalar curvature equation, and obtain some nonexistence results for complete solutions of scalar curvature equation.

Paper refines Chen-Cheng's estimates for Kähler metrics.

In this note, we obtain a sharp volume estimate for complete gradient Ricci solitons with scalar curvature bounded below by a positive constant. Using Chen-Yokota's argument we obtain a local lower bound estimate of the scalar curvature for the Ricci flow on complete manifolds. Consequently, one has a sharp estimate of…

Estimates mean curvature, scalar curvature, shape operator in warped products.

Sharp curvature estimates for expanding Ricci solitons in various dimensions.

Estimates scalar curvature on moduli space as genus grows.

Estimates scalar curvature without nonnegativity, showing gap phenomenon on manifolds.

Estimates scalar curvature of point clouds without embedding.

We establish interior $C^2$ estimates for convex solutions of scalar curvature equation and $σ_2$-Hessian equation. We also prove interior curvature estimate for isometrically immersed hypersurfaces $(M^n,g)\subset \mathbb R^{n+1}$ with positive scalar curvature. These estimates are consequences of an interior estimate…

The paper improves curvature estimates for Ricci flow solutions with bounded scalar curvature.

The paper establishes distance estimates for manifolds with lower scalar curvature bounds.

Upper bound found for systolic geometry on manifolds with positive scalar curvature.

New decay estimates for scalar curvature of steady gradient Ricci solitons.

Study on gradient h-almost Yamabe solitons with scalar curvature estimation.

We prove a priori interior curvature estimates for hypersurfaces of prescribing scalar curvature equations in dimension three. The method is motivated by the integral method of Warren and Yuan. The new observation here is that the "Lagrangian" submanifold constructed similarly as Harvey and Lawson has bounded mean curv…

The paper explores geometry and positive scalar curvature on non-compact manifolds.

New proof for curvature and diameter estimates on Fano manifolds.

Study on positive scalar curvature and its impact on Ricci limit spaces.

We prove existence in the Minkowski space of entire spacelike hypersurfaces with constant negative scalar curvature and given set of lightlike directions at infinity; we also construct the entire scalar curvature flow with prescribed set of lightlike directions at infinity, and prove that the flow converges to a spacel…

Study on 3-manifolds with nonnegative scalar curvature and positive harmonic functions.

Study pinches curvature under Laplacian G_2 flow, proving Weyl tensor norm blows up.

Sharp estimate for 2-systole on Kähler surfaces with positive scalar curvature.

We obtain a priori estimates for solutions to the prescribed scalar curvature equation on $S^3$. The usual non-degeneracy assumption on the curvature function is replaced by a new condition, which is necessary and sufficient for the existence of a priori estimates, when the curvature function is a positive Morse functi…

On Riemannian manifolds of dimension 4, for prescribed scalar curvature equation, under lipschitzian condition on the prescribed curvature, we have an uniform estimate for the solutions of the equation if we control their minimas.

Paper examines conditions making Riemann solitons trivial and estimates their scalar curvature.

The study examines how average scalar curvature influences geometric properties of Riemannian manifolds.

The paper characterizes solitons and estimates scalar curvature.

We prove a priori estimates for constant Chern scalar curvature metrics on a compact complex manifold conditional on an upper bound on the entropy, extending a recent result by Chen-Cheng in the Kähler setting.

Upper estimate of Dirac eigenvalue linked to hyperspherical radius.

Sharp gradient estimate for scalar curvature on 3-manifolds.

The study explores positive scalar curvature metrics on non-orientable manifolds and their covers.

Developing a singular dimension descent method for positive scalar curvature obstructions

The paper studies 3D manifolds with positive scalar curvature and volume growth.

In this paper, we derive apriori estimates for constant scalar curvature Kähler metrics on a compact Kähler manifold. We show that higher order derivatives can be estimated in terms of a $C^0$ bound for the Kähler potential. We also discuss some local versions of these estimates which can be of independent interest.

The paper proves estimates for Hermitian metrics and shows curvature blow-up on complex manifolds.

In this paper, we first derive a pinching estimate on the traceless Ricci curvature in term of scalar curvature and Weyl tensor under the Ricci flow. Then we apply this estimate to study finite-time singularity behavior. We show that if the scalar curvature is uniformly bounded, then the Weyl tensor has to blow up, as …

Paper proves a Liouville theorem for solitons with constant curvature.

Paper proves mass theorems for nonnegative scalar curvature metrics.

Study negative scalar curvature metrics with positive boundary mean curvature.

The paper proves inequalities for scalar curvature on various manifolds.

The paper explores rigidity theorems for spectral curvature bounds in 3-manifolds.

Paper sharpens inequality linking curvature and spectrum on manifolds.

Estimates Bartnik mass for metrics with nonnegative Gauss curvature.

We consider an asymptotically flat Riemannian spin manifold of positive scalar curvature. An inequality is derived which bounds the Riemann tensor in terms of the total mass and quantifies in which sense curvature must become small when the total mass tends to zero.

Optimal diameter estimates for 3D spaces with non-negative Ricci curvature.